a car starts from a point at 2:00 p.m. and travels north at 40 mph. another car starts from the same point at 3:00 p.m. and travels west at 50 mph. after the second car has traveled 1 h, at what rate is the distance between the two cars changing?

The area of the circle is 64π square unit and the circumference is 16π units

From the question, we are to find the area and circumference of the circle

The area of a circle is given by the formula,

A = πr²

Where A is the area

and r is the radius

Using the parameter, radius = 8

Then,

A = π × 8²

A = 64π square unit

Calculating the circumference

The circumference of a circle is given by the formula

C = 2πr

Where C is the circumference

and r is the radius

Thus,

C = 2  × π × 8

C = 16π units

Hence, the area of the circle is 64π square unit and the circumference is 16π units

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The codes of the countries are 34, 35 and 36

The given parameters are

Sum of codes = 105

Where the numbers are consecutive numbers

This means that

B = A + 1

C = A + 2

So, we have

A +A + 1 + A + 2 = 105

Evaluate the like terms

3A = 102

Divide through by 3

A = 34

So, we have

B = A + 1 = 34 + 1 = 35

C = A + 2 = 34 + 2 = 36

Hence, the codes of the countries are 34, 35 and 36

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The perimeter of the rectangle is P = (17.2x₊16.4).

Given that,

Length, l = 8.6x₊3

Width, b = 5.2

In the formula P=2l+2w, where l is the rectangle's length and w is its width, the perimeter P of a rectangle is determined. Using the formula A=l×w, where l is the length and w is the width, we can determine the area A of a rectangle.

We need to find the expression for the perimeter of the rectangle. The formula for the perimeter of the rectangle is given by :

P=2(l₊b)

Putting values of l and b in the above formula:

p = 2(8.6x ₊ 3 ₊ 5.2)

= 2(8.6x ₊ 8.2)

= 2(8.6x) ₊ 2(8.2)

= 17.2x ₊ 16.4

So, the required perimeter of the rectangle is 17.2x₊16.4.

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Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the roots are given as follows:

Hence the polynomial is given as follows, considering leading coefficient a = 1:

[tex]f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)[/tex]

His error was at the application of the minus signal to the complex roots.

Then:

f(x) = (x - 3)[(x - 2)² - (2i)²]

f(x) = (x - 3)(x² - 4x + 4 + 4)

f(x) = (x - 3)(x² - 4x + 8)

f(x) = x³ - 7x² + 20x - 24.

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Converting 140 kilometers to miles, the distance from a road sign in Canada to Toronto is 87 miles.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

From the problem, we must convert the distance of 140 kilometers into miles.

Converting kilometers to miles, we must use the conversion

1 kilometer = 0.621371 mile

140 kilometers = 140 (0.621371 mile)

140 kilometers = 86.992 miles

Rounding off to the nearest mile,

140 kilometers = 86.992 miles = 87 miles

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Answer:

p = 2 + l w

Step-by-step explanation:

Answer:

It's really hard to really solve cause I'm a student in learning.

Answer: 15

Step-by-step explanation:

Distance formula: a^2+b^2=c^2 where c is the distance.

a^2=

(-6-3)^2=

(-9)^2=81

b^2=

(5-(-7))^2=

(5+7)^2=

12^2=144

c^2=81+144=225

If c^2=225, then what's c?

c=15

Answer:

the numerator (the top number)/ Denominator (bottom number)

Step-by-step explanation:

you should know this

Answer:

Fractional mathematics have to do with dealing with certain amounts of a number and mathematical proportions. Fractions are amounts out of a whole number.

It appears that from graph that the function is increasing in the interval (-∞,-1) and (1,∞). Also the function is decreasing in the interval (-1,1) and (0.0.5).The function is not constant anywhere.

To check if this is correct, we will find the relative extrema of the function,

f(x) = x³-x²-2x+3

Find it derivative f'(x) = 3x²-2x-2

f'(x) = 0

⇒ x = 2 ± √(4+24)/3

      = 3.77 , -1.1

Find the second derivative f''(x) = 6x -2

f''(3.77) = 20.62>0

So the function has a relative minimum at x = 3.77.

f''(-1.1) = -8.6<0

So the function has a relative maximum at x = -1.1

Now we can conclude with the intervals where the function is increasing is before the relative maximum and after the relative minimum.

i.e., the intervals (-∞,-1) and (3.5,∞) [rounding to the nearest 0.5 unit]

So the interval in which the function is decreasing is between the relative maximum and minimum. i.e.,  the interval (-1, 3.5)

The function is nowhere constant.

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Final answer:

The estimated number of days the aqi was over 100 in the year 1995 is calculated as 135 days.

Simple linear regression is expanded upon in quadratic regression. While quadratic regression has the drawback of requiring more data points to ensure that your data falls into the "U" shape, linear regression can be carried out with as few as two points (i.e., enough points to draw a straight line).

In situations where the second differences are constant, a quadratic model is adequate. We can ascertain the degree of the model for the data by identifying variations between the dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.

Explanation:

The air quality index, or aqi, calculates a number depending on how clean or dirty the air. Then it is estimate n, the number of days the aqi exceeded 100 in a specific year is evaluated and calculated as it is actually as 135 days on edge.

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The mass of pyramid is 6 grams and the cube is 8 grams

Let's assume the mass of a pyramid is x gram and mass of a cube is y gram .

So, algebraic mass of 6 and 4 pyramids is 6x grams and 4x grams. and algebraic mass of 2 cubes and 4 cubes is 2y grams and 4y grams .

Total algebraic mass of 4 pyramids and 2 cubes are , 4x + 2y = 40 ;(equation 1)

and Total algebraic mass 6 pyramids and 4 cubes are , 6x + 4y = 68 ;(equation 2)

Now we have to use adoption method to solve this problem ,  

we have to multiply equation (1) with 4 and equation (2) with 2 , and we will get ,

16x + 8y = 160 ; ( equation 3 )

12x + 8y = 136 ; ( equation 4 )

Now , we will substract equation ( 3 ) from equation ( 4 )

4x = 24 and x = 24/4 = 6

Let's put the value of x in equation ( 1 )

24 + 2y = 40 or, 2y = 16 or, y = 8

Here we can conclude , mass of pyramid is 6 grams and the cube is 8 grams.  

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Using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.

The distance formula is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the following locations:

P(1,17) = (x1, y1)

Q(12,10) = (x2, y2)

Use the distance formula to find the PQ:

PQ = √[(12−1)² + (10−17)²]

PQ = √[(11)² + (−7)²]

PQ = √170

PQ ≈ 13.04 units

1 unit = 100 miles

PQ = 13.04 × 100

PQ = 1,304 mils

Thus, using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.

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Answer: B. 1,304 miles.

The probability that at least one of them is operational is 0.999

Probability:

Probability means the possibility of happening the particular event. So, it can be written as the fraction of possible event by the total number of event.

Given,

The probability a D-Link network server is down is 0.10.

Here we need to find if you have three independent servers, what is the probability that at least one of them is operational.

Let D be an event that a D-Link network server is down.

It is given that the probability that a D-Link network server is down is

=> P(D) = 0.10

The number of independent servers

=> (n) = 3

The probability that none of the servers is working is

=>P(None) = P(D) x P(D) x P(D)

=> P(None) = 0.10 x 0.10 x 0.10

=> P(None) = 0.001

The probability that at least one of them is operational is given as

=> 1 - P(None)

=> 1 - 0.001

=> 0.999

Therefore, the probability that at least one of them is operational is 0.999.

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Answer:

i think b

Step-by-step explanation:

Answer:

B. y = 2x + 8

Step-by-step explanation:

14x - 7y = 1

7y = 14x - 1

y = 2x - 1/7

If two lines are parallel, their slopes are equal.

With m = 2, x = -2, y = 4

y = mx + b

4 = 2(-2) + b

4 = -4 + b

b = 8

so y = 2x + 8

Using the function concept, we have that:

A relation represents a function when each value of the input is mapped to only one value of the output.

On a graph, it means that each value of x is mapped to only one value of y, that is, there are no vertically aligned points on the graph.

For this problem, relation c does not represent a function, as there are multiple values of x are related to two values of y, and there are vertically aligned points on the graph.

In item b, when x = 6, there are two values of y, hence this is also not a function. For items a and d, each value of x is mapped to only one value of y, hence they are functions.

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The percentage of u.s. land is national park system land is approximately 41.8%

Convert acres to square miles

Percentage of u.s. land is national park system land = national park system land / Total U.S. land area × 100

= 1476562.5 square miles / 3,537,000 square miles × 100

= 0.417461832061068 × 100

= 41.74618320610687%

Approximately,

41.8%

Therefore, the percentage of u.s. land is national park system land is approximately 41.8%

Complete question:

Total U.S. land area is 3.537 million square miles. Total U.S. national park system land occupies 954 million acres. What percentage of U.S. national park system land?

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Answer:

0.0416¯

Step-by-step explanation:

after the 1 six is being repeated. Hope this helps! :)

The number 86,360,000 using the number word "million" and then round to one decimal place is Eighty-six million three hundred sixty thousand.

The writing style used to express numbers in India is known as the Indian numeral system. In this case, numbers are divided into several time periods or groupings. This numbering scheme uses ten distinct symbols, including the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

The order of the digits when using the Indian number system is one, ten, hundreds, thousands, ten thousand, lakhs, lakhs, crores, and crores. The era and locations are shown in the table below according to the amount of digits in a number.

Given number: 86,360,000

Eighty-six million three hundred sixty thousand in numbers

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The coordinates of the point where the chain should attach to the triangle are (3, 4).

Given that, a triangle is on a coordinate plane with coordinates (0,4), (3,8), and (6,0).

We need to find the coordinates of the point where the chain should attach to the triangle.

The centroid is the centre point of the object. The point at which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle formula is G = ((x1+x2+x3)/3 , (y1+y2+y3)/3).

Now, centroid = ((0+3+6)/3, (4+8+0)/4)

=(3, 4)

Therefore, the coordinates of the point where the chain should attach to the triangle are (3, 4).

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The student did the subtraction step of PEMDAS out of order.

PEMDAS is a rule regarding precedence of operations, given as follows, from highest to lowest precedence.

In this problem, the expression is:

(6 - 2)² + 12  - 3².

The student reached an answer of 97 as follows:

(6 - 2)² + 9² = 4² + 9² = 16 + 81 = 97.

The student did the subtraction first, hence the student did the subtraction step of PEMDAS out of order.

The correct solution is:

(6 - 2)² + 12  - 3² -> Solve the Parenthesis.

4² + 12 - 3² -> Solve the Exponents.

16 + 12 - 9 -> Solve the Addition and Subtraction.

19.

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Answer:

-1

Step-by-step explanation:

-1 has the greatest value

Bob after downloading the valid data set from the internet and calculating the correlation values as 0.5 concludes that as the number of bedrooms in a home increases its selling price also increases.

This happens because as there is an increased demand for the number of bedrooms in a home there should be enough supply in the market to fulfill the requirements. So, there should be a surplus of beds in the market and for that the selling price increases to maintain the surplus.

The law of Demand states that as the demand for a particular commodity or a product increases its price also increases. The above example of Bob gets verified according to the Law of Demand.

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If total cost for tuition plus room and board at state university is 2,584 dollars and  tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars

Given,

The total cost for tuition plus room and board = 2584 dollars

Consider the cost for room and board as x

Tuition costs 704 dollars more than room and board.

Therefore the tuition fees = 704+x

Then the total cost = Cost for tuition fees+ Cost for room and board

2584 = (704+x)+x

2584= 704+2x

2x= 1880

x= 940  dollars

Then the tuition fees = 704+x

=704+940

=1644 dollars

Hence, if total cost for tuition plus room and board at state university is 2,584 dollars and  tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars

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i) 9⁻⁴=1/6561

ii1/2⁻⁶=64

Positive exponent: An exponent defines the number of times a number is multiplied by itself. For example, 32. It means that the number 3 has to be multiplied twice. Here, the number 3 is a base number and 2 is an exponent. The exponent can be positive or negative.

Nagative exponent: We know that the positive exponent tells us how many times a number is multiplied by itself. Whereas, the negative exponent tells us how many times we have to divide the base number. In other words, the negative exponent describes how many times we have to multiply the reciprocal of the base. An example of negative exponents is 3-2.

Thus, x-2 is written as (1/x²).

i)Rewrite expression using a positive exponent  9⁻⁴

We know that positive exponent.

9⁻⁴=1/94

9⁻⁴=1/6561.

ii)Rewrite expression using a positive exponent 1/2⁻⁶

1/2⁻⁶=26

⇒1/2⁻⁶=64.

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The LCM of 8a²b³f⁴ and 3abg is 24a²b³f⁴g.

LCM is an abbreviation for "Least Common Multiple." The smallest multiple which two or even more numbers have in common is defined as the least common multiple.

Figuring the lowest common denominator (LCD) of 2 or even more fractions is a common application of LCM.

It is useful for adding, subtracting, as well as compare different or more fractions.

For the given question, the two numbers are given as; 8a²b³f⁴ and 3abg.

The least common multiple which will divide both the numbers are; all the values with their highest power.

LCM = 24a²b³f⁴g.

Thus, the LCM is found as 24a²b³f⁴g.

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The graph is plotted in the following figure .

To plot a graph we need 2 pts .

First eqn is of a circle ( [tex]x^{2}[/tex] ) + ( [tex]y^{2}[/tex] ) = 4

Second eqn is of a line x - y = 1

The center of circle is ( 0 , 0 )

The circle passes through ( 2 , 0 ) , ( 0 , 2 ) , ( - 2 , 0 ) , ( 0 , - 2 ) .

The line passes through ( 0 , 1 ) , ( 0 , - 1 ) .

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